Photoelectron data for hollow lithium states obtained with unprecedented high spectral resolution and sensitivity are presented. A critical comparison is made with the most recent theoretical results. Partial cross sections are measured providing the first definitive test of advanced ab initio calculations for this highly excited four-body atomic system

A. Hibbert

A. Muller

A. S. Schlachter

B. Rouvellou

C. A. Nicolaides

C. Blancard

D. Cubaynes

D. R. Herrick

E. T. Kennedy

F. J. Wuilleumier

F. T. Smith

G. Kaindl

G. Mehlman

H. R. Sadeghpour

J. Bozek

J. P. Briand

J.-M. Bizau

K. T. Chung

L. Journel

L. M. Kiernan

L. VoKy

L. Voky

M. Rodbro

N. A. Piangos

N. Berrah

P. Faucher

R. Bruch

R. L. Simons

S. Al Moussalami

S. Diehl

T. J. Morgan

U. I. Safronova

Y. Azuma

Diehl, S.

Cubaynes, D.

Bizau, J.-M.

Journel, L.

Rouvellou, B.

Al Moussalami, S.

Wuilleumier, F.

Kennedy, Eugene T.

Berrah, N.

Blancard, C.

Morgan, T.

Bozek, J.

Schlachter, A.

VoKy, L.

Faucher, P.

Hibbert, A.

DCU Online Research Access Service

VOLUME 76, NUMBER 21 P HY S I CA L REV I EW LE T T ER S 20 MAY 1996High Resolution Measurements of Partial Photoionization Cross Sections in Hollow Lithium:A Critical Comparison with Advanced Many-Body CalculationsS. Diehl, D. Cubaynes, J.-M. Bizau, L. Journel, B. Rouvellou, S. Al Moussalami, and F. J. WuilleumierLaboratoire de Physique Atomique et Ionique, Université Paris Sud, B. 350, 91405-Orsay Cedex, FranceE. T. KennedyDublin City University, Glasnevin, Dublin 9, IrelandN. BerrahUniversity of Western Michigan, Kalamazoo, Michigan 40849C. BlancardCEA, Centre d’Etudes Nucléaires de Limeil-Valenton, 94195 Villeneuve, St. Georges Cedex, FranceT. J. MorganWesleyan University, Middletown, Connecticut 06459J. Bozek and A. S. SchlachterLawrence Berkeley Laboratory, Advanced Light Source, University of California, Berkeley, California 97420L. VoKy and P. FaucherObservatoire de la Côte d’Azur, BP 229, 06304 Nice Cedex, FranceA. HibbertQueen’s University of Belfast, Belfast, Northern Ireland(Received 29 December 1995)Photoelectron data for hollow lithium states obtained with unprecedented high spectral resolution andsensitivity are presented. A critical comparison is made with the most recent theoretical results. Partialcross sections are measured providing the first definitive test of advanced ab initio calculations for thishighly excited four-body atomic system. [S0031-9007(96)00241-4]PACS numbers: 32.80.Fb, 32.80.HdIn this Letter, we present photoelectron data for hollowlithium states obtained with unprecedented spectral reso-lution (0.019 eV) and sensitivity which allows a criticalcomparison with the most advanced recent theoretical cal-culations. The partial cross sections are measured and res-onance profile parameters are determined. In addition, wehave used the R-matrix approximation to calculate ab initiothe partial photoionization cross sections into all contin-uum channels of the Li1 ion over a wide photon energyrange. The experimental results provide the first definitivetest of such advanced calculations for this highly excitedatomic system.The photoexcitation and decay dynamics of hollowlithium atoms, in which all three electrons are in excitedstates, have become the subject of intense recent experi-mental and theoretical interest. The single-photon three-electron excitations depend entirely on electron-electroncorrelation interactions and so hollow lithium atoms con-stitute an ideal four-body Coulomb system for testingthe most advanced atomic theories. Following the firstphoton-excited observation [1] of the lowest hollow atomresonance (1s22s 2S ! 2s22p 2P), two total ion yieldphotoion experiments at high [2] and medium [3] spectral0031-9007y96y76(21)y3915(4)$10.00resolution measured the autoionization of several hollowstates in both the Li1 and Li21 decay channels. Photo-electron spectrometry [4] was also used with low resolu-tion to study the decay of the hollow lithium 2s22p stateinto the different continua of the Li1 ion. The 0.5 eVspectral bandpass of the latest experiment however lim-ited the critical nature of the comparison with theory.Double K-shell excitations in atomic helium have cul-minated in recent ultrahigh resolution measurements [5].The third electron makes the theoretical and experimen-tal study of hollow lithium states an even greater chal-lenge than that of helium. Although triply excited statesof lithium were first observed in collision experiments [6–8], only photon-excitation experiments provide the selec-tivity, sensitivity, and resolution required to unravel themany hollow lithium resonances. The dipole selectionrules ensure that only 2Po final states can be photoexcitedfrom the ground state of the lithium atom. Photoelectronspectrometry combines the advantages of photon excita-tion with the unique capacity to measure separately themany decay channels and to provide insight into decaydynamics. The key role played by hollow atom states inion-surface interactions has also been recognized [9].© 1996 The American Physical Society 3915VOLUME 76, NUMBER 21 P HY S I CA L REV I EW LE T T ER S 20 MAY 1996The previous photoelectron spectrometry measurements[4] were carried out at the SuperACO storage ringat Orsay with modest resolution (0.5 and 0.23 eV onthe bending magnet and undulator beam, respectively).The present experiments were performed on beam line9.0.1 at the Advanced Light Source in Berkeley, whichprovides the most intense source available of highlymonochromatic light in this energy range. The very highphoton beam brightness (.1012y sec in 20 meV spectralwidth at 150 eV) allowed a number of very significantimprovements to be made. The bandpass of the electronspectrometer was reduced by a factor of 2 (0.45% ofthe electron energy) allowing better discrimination of thedecay channels. The maximum spectral resolution wasimproved by a factor of 10 (0.019 eV). Many of themeasurements were carried out with a spectral resolutionof 40 meV. Furthermore, the high photon flux allowedthe use of lower atomic densities which resulted in verylow background count levels in our experiments. Therelative partial cross sections were measured by constantionic state spectroscopy. The statistical error was about3%. The total uncertainty on the relative values of thepartial cross sections is usually less than 10%. They wereput on an absolute scale by normalizing the data measuredat 110 eV to the photoabsorption cross section [10], whichintroduces an additional uncertainty of 25%.Several approximations have been exploited to computethe energies (and sometimes the widths) of a number ofmultiply excited states in lithium [11–15]. It is, how-ever, only the most recent developments in R-matrix the-ory which have allowed a comprehensive photoionizationcalculation including resonances to be carried out. Appli-cation of the code to inner-shell photoionization involvesspecific difficulties, previously described [16]. Initial R-matrix results for lithium have already been reported [4].Here, we present a comparison of our high-resolution re-sults with the theoretical values of several partial cross sec-tions over a wider range of photon energies. The recentexperimental results on hollow lithium have also stimu-lated very detailed calculations with the saddle-point andsaddle-point complex-rotation methods [13,17].In Fig. 1, we show the measured variation of the partialcross section for photoionization into the 1s2p 1P 1 «schannel in the vicinity of the 2s22p 2P resonance andcompare it with the R-matrix results. The agreement interms of the resonance width and profile and the relativeamplitude of the cross section is impressive. With regardto the absolute value of the cross section, the theoreticalresult is about 50% higher than the measured value,while the total experimental uncertainty is close to 35%.The measured absolute energy of the resonance differsfrom the R-matrix value by 0.13 eV. Using the Fano-Starace formulation for deconvoluting the instrumentalprofile (0.019 eV), a FWHM of 0.118 6 0.003 eV isobtained for the 2s22p 2P resonance profile. In Table I,we show a comparison between the present and previousmeasurements together with recent theoretical results.3916FIG. 1. The experimental photoionization cross section oflithium to the 1s2p 1P ionic state (upper part) compared withthe result of the ab initio R-matrix calculation (lower part), inthe vicinity of the lowest hollow atom state (2s2p 2P).The present high spectral resolution experiment succeedsin determining the profile width with an uncertainty suffi-ciently small (the smallest to date) to test the most recenttheoretical calculations. Our results agree extremely wellfor both the resonance energy and width, with the veryrecent high precision calculation using the saddle-pointtechnique [17]. The partial cross-section behavior for de-cay of this state to 1s2s 3S 1 «p shows an asymmetricprofile due to the strong interaction with the direct pho-toionization process in this channel. The deconvolutedwidth of 0.122(5) eV is consistent with that determinedfrom the more symmetric 1s2p 1P channel.The previous photoion experiments [2,3] demonstrateda rich spectrum of multiply excited states in the 145–165 eV energy region. Because of cancellation effectsparticular resonances may sometimes be very weak insuch experiments but be large if observed in a specificdecay channel as in a photoelectron experiment; appli-cation of photoelectron spectroscopy to these higher ly-ing resonances is therefore particularly advantageous. InFig. 2 we show, as examples, the decay into the 1s3s 3Sand 1s2p 1,3P channels, for the energy range 140.4–154 eV which encompasses many of the hollow atomstates previously observed in photoion experiments, to-gether with the corresponding R-matrix theoretical par-tial cross-section results. Apart from an energy shiftof 0.1 to 0.3 eV, the detailed agreement (on a relativecross-section basis) is a tribute to both the quality ofthe new experimental data and the R-matrix calculations.VOLUME 76, NUMBER 21 P HY S I CA L REV I EW LE T T ER S 20 MAY 1996TABLE I. A comparison between the present experimental results and previous photoexcita-tion measurements together with a selection of theoretical results for the 1s22s 2S ! 2s22p 2Ptransition.Experimental E0 seVd G seVdThis work 142.28(3) 0.118(3)Photoabsorption [1] 142.32(3) 0.20(6)Photoion [2] 142.32(3) 0.14(3)Photoion [3] 142.35(10) 0.15(2),a 0.20(4)bPhotoelectron [4] 142.30(5) 0.20(4)TheoreticalR-matrix 142.12 0.13Saddle point [17] 142.255 0.1175Multiconfiguration Hartree-Fock [2] 141.90 0.21Multiconfiguration Dirac-Fock [3] 141.657Many-body perturbation theory [12] 142.661 0.13aPhotoion yield measurement.bLi11 (time of flight).The asymmetry of the 150 eV resonance and the detailedstructure in the neighborhood of the strong 152.4 res-onance is accurately reflected in both experimental andtheoretical curves, including the near zero minimum at152.55 eV. The latter shows however additional weakFIG. 2. Upper part: a comparison, for the 149.4–154 eV en-ergy range, of the experimental photoionization cross sectionsto the 1s3s 3S with ab initio R-matrix calculation and (lowerpart) a similar comparison for photoionization to the 1s2p 1,3Pfinal Li1 ionic states (the individual 1P and 3P patterns aresimilar).TABLE II. Assignments and energies of high-lying threeelectron transitions in atomic lithium. The energy positionmeasured in the present work are obtained from fitting a Fano-Starace–type profile.Transition Energy (eV)1s22s 2S ! High res.n,n0,0n00,00 00 2P This work photoion [3] R matrix2s2ps3Pd3s 149.98(4) 149.91 149.702s2ps3Pd4s 151.25(4) 151.20 150.972p2s3Pd3p 152.51(3) 152.46 152.412s2ps1Pd3s 152.90(5) 152.75 152.482p2s3Pd4p 153.66(5) 153.54 153.48and narrow resonances in the 1s2p 1,3P channel, whichare not fully reproduced in the experimental data due toresolution limitations. The absolute cross-section valuescalculated by the R-matrix method are again greater thanthe experimentally determined values. In Table II, wegive our energy measurements for the main resonancesobserved in this energy range. They are usually in goodagreement, within the error bars, with those previouslydetermined in the high resolution [2] photoion yieldexperiment.In order to make a comparison between our new resultand the earlier photoion work, we have summed thedifferent 2S11L decay spectra in the n ­ 2, 3, and 4channels, as shown in the three upper frames of Fig. 3.This provides a good estimate of the total photoabsorptioncross section in this spectral region as decay to higherchannels is very weak. The comparison of our resultswith the relative photoion yield data [2] confirms thatthe profiles of the resonances are very different in thedifferent channels. For example, the 152.5 resonancepredominantly decays to the n ­ 3 channels whereasthe 150 eV feature shows up strongly in the n ­ 3 andn ­ 4 channels. This pattern provides valuable clues to3917VOLUME 76, NUMBER 21 P HY S I CA L REV I EW LE T T ER S 20 MAY 1996FIG. 3. The curves shown in the three upper frames show,respectively, the experimental photoionization cross sections tothe n ­ 2, 3, and 4 states of Li1, obtained by summing the1,3L partial cross sections for each principal quantum number n.The two lower curves show the total absorption cross sectiondetermined by adding the n ­ 2, 3, and 4 cross sections and,for comparison, the photoion yield data for Kiernan et al. [2],respectively.the principal configurations in the decaying resonances.Care, however, needs to be taken in the analysis; theuniqueness of normal spectroscopic orbital labeling of theresonances (based on the independent-particle model) isquestionable in view of the strongly correlated motions ofthe hollow atom resonances. In doubly excited heliumit was found advantageous to introduce new quantumnumbers which take into account the correlated motionsof the two electrons directly [18]. In recent work onH2 [19], it was shown that the autodetaching Feshbachresonances decay primarily into the nearest energeticallyaccessible continuum channel, with similar angular andradial correlations, and the delay-time matrix [20] is veryappropriate for study of the excitation and decay of such3918quasistable states. Here, we found that it is, indeed, then ­ 4 channel in which the decay of the resonances isthe strongest on a relative scale. A calculation of triplyexcited states of lithium in hyperspherical coordinateshas been carried out recently [21]. It is expected thatfurther theoretical efforts in these directions will provideadditional physical insight into this strongly correlatedfour-body atomic system.In summary, the present experimental results providethe most stringent test to date of calculations for hollowlithium states. The R-matrix code is seen to produce re-markable agreement with the relative values of the mea-sured profile cross sections while the measured profile forthe lowest lying resonance (2s2p 2P) is in good agreementwith the saddle-point calculations.The support of the Centre d’Etudes Nucléaires deLimeil-Valenton (CEADAM), Advanced Light Source,EU Human Capital and Mobility Program under Con-tract No. 93-0361, and DOE Basic Energy Science un-der Contract No. DE-FG02-92ER14299 is gratefully ac-knowledged.[1] L.M. Kiernan, E. T. Kennedy, J.-P. Mosnier, J. T.Costello, and B. F. Sonntag, Phys. Rev. Lett. 72, 2359(1994).[2] L.M. Kiernan, M.K. Lee, B. F. Sonntag, P. Sladeczek,P. Zimmermann, E. T. Kennedy, J.-P. Mosnier, and J. T.Costello, J. Phys. B 28, L161 (1995).[3] Y. Azuma et al., Phys. Rev. Lett. 74, 3770 (1995).[4] L. Journel, D. Cubaynes, J.M. Bizau, S. Al Moussalami,B. Rouvellou, F. J. Wuilleumier, K. Voky, P. Faucher, andA. Hibbert, Phys. Rev. Lett. 76, 30 (1996).[5] G. Kaindl et al., Synchrotron Radiat. News 8, No. 5, 29(1995).[6] R. Bruch, G. Paul, J. Andra, and L. Lipsky, Phys. Rev. A12, 1808 (1975).[7] M. Rodbro, R. Bruch, and P. Bisgaard, J. Phys. B 12,2413 (1979).[8] A. Muller et al., Phys. Rev. Lett. 63, 758 (1989).[9] J. P. Briand et al., Phys. Rev. Lett. 65, 159 (1990).[10] G. Mehlman, J.M. Cooper, and E.B. Salomon, Phys. Rev.A 25, 2113 (1982).[11] U. I. Safronova and V. S. Senashenko, J. Phys. B 11, 2623(1978).[12] R. L. Simons, H. P. Kelly, and R. Bruch, Phys. Rev. A 19,682 (1979).[13] K. T. Chung, Phys. Rev. A 25, 1596 (1982).[14] C. A. Nicolaides, J. Phys. B 26, L291 (1993).[15] N. A. Piangos and C.A. Nicolaides, Phys. Rev. A 48, 4142(1993).[16] L. Voky, H. E. Saraph, W. Eissner, Z.W. Liu, and H. P.Kelly, Phys. Rev. A 46, 3945 (1992).[17] K. T. Chung and B. C. Gou, Phys. Rev. A 52, 3669 (1995).[18] D. R. Herrick and O. Sinanoglu, Phys. Rev. A 11, 97(1975).[19] H. R. Sadeghpour, C. H. Greene, and M. Cavagnero, Phys.Rev. A 45, 1587 (1992).[20] F. T. Smith, Phys. Rev. 118, 349 (1960).[21] C. D. Lin (private communication).

High resolution measurements of partial photoionization cross sections in hollow lithium: a critical comparison with advanced many-body calculations

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High Resolution Measurements of Partial Photoionization Cross Sections in Hollow Lithium: A Critical Comparison with Advanced Many-Body Calculations

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High resolution measurements of partial photoionization cross sections in hollow lithium: a critical comparison with advanced many-body calculations

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